# Difference between revisions of "ApCoCoA-1:CharP.GBasisF2"

## CharP.GBasisF2

Computing a Groebner Basis of a given ideal in F_2.

### Syntax

```CharP.GBasisF2(Ideal:IDEAL):LIST
```

### Description

Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.

This command computes a Groebner Basis in the field F_2 = Z/(2).

• @param Ideal An Ideal in a Ring over Z, where the elements 0,1 represent the elements of the field.

• @return The Groebner Basis of the given ideal.

#### Example

```Use R::=QQ[x,y,z];
I:=Ideal(x-y^2,x^2+xy,y^3);
GBasis(I);
[x^2 + xy, -y^2 + x, -xy]
-------------------------------
Use Z::=ZZ[x,y,z];
-- WARNING: Coeffs are not in a field
-- GBasis-related computations could fail to terminate or be wrong

-------------------------------
I:=Ideal(x-y^2,x^2+xy,y^3);
CharP.GBasisF2(I);
-- WARNING: Coeffs are not in a field
-- GBasis-related computations could fail to terminate or be wrong
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
[y^2 + x, x^2, xy]
-------------------------------
```